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Question
(p ∧ q) → r is logically equivalent to ________.
Options
p → (q → r)
(p ∧ q) → ∼r
(∼p ∨ ∼q) → ∼r
(p ∨ q) → r
Solution
(p ∧ q) → r is logically equivalent to p → (q → r).
Explanation:
(p ∧ q) → r: For r to hold, both p and q together must imply r. If either p or q is false, (p ∧ q) is false and implication automatically holds true.
p → (q → r): For r to hold, p must imply that q implies r. If p is false, the implication automatically holds true. If p is true, then q → r must hold.
Both statements represent the same logical condition, making them logically equivalent.
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